A unified analysis of FBP-based algorithms in helical cone-beam and circular cone- and fan-beam scans

A circular scanning trajectory is and will likely remain a popular choice of trajectory in computed tomography (CT) imaging because it is easy to implement and control. Filtered-backprojection (FBP)-based algorithms have been developed previously for approximate and exact reconstruction of the entire image or a region of interest within the image in circular cone-beam and fan-beam cases. Recently, we have developed a 3D FBP-based algorithm for image reconstruction on PI-line segments in a helical cone-beam scan. In this work, we demonstrated that the 3D FBP-based algorithm indeed provided a rather general formulation for image reconstruction from divergent projections (such as cone-beam and fan-beam projections). On the basis of this formulation we derived new approximate or exact algorithms for image reconstruction in circular cone-beam or fan-beam scans, which can be interpreted as special cases of the helical scan. Existing algorithms corresponding to the derived algorithms were identified. We also performed a preliminary numerical study to verify our theoretical results in each of the cases. The results in the work can readily be generalized to other non-circular trajectories.